This seems to violate the spirit of a consistent classical theory of charged particles, as enunciated by Rohrlich. Correspondingly, we make no assumption that the fifth dimension is compact, since that is not necessitated by the Kaluza field equations or by the cylinder condition [1]}. This work is not “Kaluza-Klein” theory, but the strictly classical Kaluza theory of 5D general relativity. The conceptual framework we adopt for the fixed mathematics is that the fifth dimension is open and macroscopic, like the other four of spacetime. No macroscopic classical experiment contradicts that assumption. Classical theories can only be tested in classical experiments. As we will see, the cylinder condition produces a non-trivial constant of the motion irrelevant to compact dimensions.
